线性

We first state general linear model, ridge-type estimator and general ridge-type estimator, and the constraint biased estimator. And then, we introduce some basic theory about matrix and some conclusion about the admissibility of estimator in Gauss-Markov model. In the third chapter, we discussion several equivalent characterization of the best linear unbiased estimation, we proved that admissible characterization of admissible of linear estimation is as conditional general ridge-type estimation in general linear model. A necessary and sufficient condition that homogeneous linear estimator is admissible estimator is obtained.

本文首先概述了一般线性模型，岭估计及约束岭估计的发展历史和研究现状，在第二章介绍了矩阵的一些基本知识和可容许性的一些基本结论，第三章讨论了一般线性模型最佳线性无偏估计的几个等价条件，以及线性估计的可容许性特征，得到了一般线性模型的可容许线性估计均具有条件广义岭估计的形式，给出了一个齐次线性估计为可容许估计的充分必要条件。

In the fourth chapter, we discussion the characterization of admissible in the general linear model under equality constraint and inequality constraint, we give the necessary and sufficient condition that homogeneous linear estimator is admissible estimator, and by using the relationship between homogeneous and inhomogeneous linear estimator, we obtain the characterization of admissible inhomogeneous linear estimator.

第四章分别在带等式约束条件以及不等式约束条件下，讨论了一般线性模型线性估计的可容许性特征，给出了在约束条件下齐次线性估计为可容许估计的充分必要条件，同时利用齐次线性估计与非齐次线性估计之间的关系，把齐次线性估计的可容许性特征推广到了非齐次线性估计的可容许性特征。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

The representation of sequences is very helpful for the research of their linear complexity,so this paper we first research trace representation of periodic sequences,and the trace representation of a New Generalized Cyclotomic Sequence of order two of length pq is given,then for 2~mp~n period binary sequences,where p is an odd prime and 2 is a primitive root modulo p~2,we present a relation-ship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity and have the upper bound and lower bound of the value k, finally we discuss the k-error linear complexity of legendre sequences,also have the upper bound and lower bound of the value k,and discusses the situation where the linear complexity drop again for some Legendre sequences.

序列的表达形式对于其线性复杂度的研究是十分有帮助的，本文我们首先研究的是周期序列的迹表示，给出了2阶pq长度的扩展分圆序列的迹表示，然后讨论了周期为2~mp~n(m≥2)序列的线性复杂度与使得线性复杂度变小的最小的k值的关系，给出了k值的上界和下界，这里p为奇素数，2是模p~2的本原根，并通过例子讨论了其线性复杂度的稳定性，最后对Legendre序列k-错线性复杂度进行了分析，也给出了k值的上界和下界，并对某些Legendre序列讨论了线性复杂度再次下降的情况。

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

Generalized linear models, which can model a large variety of data, have a wide area of application. The class of GLMs includes, as special cases, linear regression, analysis-of-variance models, log-linear models for the analysis of contingency tables, logistic models for binary data in the form of proportions and many others. Usually, the parameters in the generalized linear models are estimated by the method of maximum likelihood . But, in the literature, the nonrobustness of the maximum likelihood estimator forβhas been studied extensively. The quasi-likelihood estimator of the parameter of the generalized linear model shares the same non-robustness properties.

广义线性模型，可用于对多种类型的数据进行建模，是应用非常广泛的模型，线性回归模型、方差分析模型、用于列联表分析的对数线性模型和逻辑斯谛模型等都是广义线性模型的特例，通常，我们用极大似然的方法估计广义线性模型中的参数，但是，在文献中，对参数β的极大似然估计的非稳健性已经有了广泛的研究，广义线性模型的拟似然估计也显示了非稳健性。

This chapter defines the conceptsof P linear operator,〓 linear operator and 〓 linear operator by extending theconcepts of P matrix,〓 matrix and 〓 matrix to the linear operator from thelinear space of symmetric matrices to itself.In this chapter,we also present a path-following method and a potential reduction method for solving general linear matrixcomplementary problems,and analyzes their computational complexities undersuitable assumptions.

本章将第二章中给出的P矩阵、〓矩阵及P矩阵的概念推广到由实对称矩阵构成的向量空间到其自身的线性算子L上，得到了P线性算子、〓线性算子及P线性算子的概念，给出了求解一般线性矩阵互补问题的路径跟踪法和势函数约减法，并在L为P线性算子的假设下分析了这些算法的计算复杂性。

Unitary linear regression is done between w~e、 w~ρ、 e~ρ、w_L~w_P. For α_v 、 C_ c between w、ρ、 e、 w_P in eastern China, unitary linear regression is done to silty clay as well as multivariant regression with coefficient iteration method and least-squares procedure are done to all kinds of soil, and the two results are compared. Unitary linear regression and multivariant regression are done to c_q、φ、 c_d、φ_d between e and I_P. Unitary linear regression and multivariant linear regression are done to napierian logarithm of q_u between e 、 I_L、 w_P and w_L, then the equations of regression are checked with other parameters.

对物理指标含水量～孔隙比、含水量～湿密度、孔隙比～湿密度、液限～塑限作了一元线性回归；对华东地区粉质粘土的压缩系数、压缩指数和含水量、湿密度、孔隙比及塑性指数作了一元线性回归；对华东地区所有土类的压缩系数、压缩指数和物理性质参数用系数迭代法和最小二乘法作了多元线性和非线性回归，并对两种方法得到的回归结果作了比较；作了快剪强度指标和固结快剪强度指标关于孔隙比和塑性指数的一元线性回归和多元线性及非线性回归；对无侧限抗压强度的自然对数值和孔隙比、液性指数、液限及塑限作了一元和多元线性回归，并用其它工程的参数对回归方程进行了检验。

Modeling and stability analysis problem of linear switched system are emphasized in this part and main results include:(1) Through investigation in the projection of 〓 on x, where x denotes continuous state vector, a series of sufficient conditions for stability, asymptotic stability and unstability of linear switched system's equilibrium in the sense of Lyapunov are achieved. And also, a sufficient and necessary condition for state bounded stability of linear switched system is received.(2) For a class of periodical linear switched system whose switching sets are a group of ordinal lines starting from the original point, it's proved that state bounded stability can be defined by the running characteristic in a single period (3) Based on linear switched system, the concept of linear switched system network is put forward. Linear switched system network is a complex network interconnected by many linear switched systems.

这部分着重研究线性切换系统的建模与稳定性分析问题，主要成果包括：（1）通过考察〓在x上的投影，得到线性切换系统的平衡点在Lyapunov意义下稳定、渐近稳定及不稳定的一系列充分条件，并得到了线性切换系统状态有界稳定的一个充要条件；（2）证明了对于一类切换集为从原点出发的一组射线的周期线性切换系统，其状态有界稳定可根据一个周期内的系统运行特性来判定；（3）在线性切换系统的基础上提出了线性切换系统网络的概念，线性切换系统网络是由多个线性切换系统交互作用而形成的复杂网络。

To solve the exsisting problems in the realization of the LFM/CW radar, the thesis presents a technique for dynamically measuring the LFM/CW signals, which can accomplish the dynamic measurements of FM linearity, FM bandwidth and FM slop of the transmitted signals of LFM/CW radars. This technique creates an effective and accurate means of judging the performance of LFMCW radars. The linearity-correction techniques presented in the thesis successfully make the linearity of the transmitted signals of an actual LFM/CW radar reduce from approximately 25% to 0. 1%(or r. m. s linearity of 0.04%), better than the best results (0.22%) obtained by foreign researchers with complex linearization closed-loop in the same kind of LFM/CW radars, according to the published literatures during the last decade. In order to improve the capability of the real-time processing and range-cells management of LFM/CW radars, the principle of equivalent mixing by lacking-sampling process of band-pass real signals is proposed based on the well-proved improvedversion of sampling theorem of band-pass real signals. This principle is used to configure the range-segments processing of the beat signals of an actual LFM/CW radar. The techniques of system-background interference suppression and the beat signal's dynamic range suppression are proposed, and are realized in an actual LFM/CW radar to demonstrate their effectiveness.

针对线性调频连续波雷达实现中急待解决的技术问题，文中提出并验证了线性调频连续波信号的综合动态测试技术，可以完成对线性调频连续波雷达发射信号的扫频线性度、扫频带宽和扫频斜率的综合动态测试，为衡量实际线性调频连续波雷达的系统性能创立了精确有效的测试手段；文中建立的非实时闭环动态校正技术使一部实际的线性调频连续波雷达的发射信号（时带积3×10〓）的扫频线性度从25%改善为0.1%（方均根线性度0.04%），优于国外已公布的80年代同类雷达中采用复杂的实时闭环动态校正环路所获得的实际结果（0.22%）；为了改善线性调频连续波雷达的实时性和分辨单元数处理能力，文中发展完善了实带通信号的采样定理并给予了严格证明，并在此基础上提出了欠采样等效混频原理，将其应用于实际线性调频连续波雷达的距离分段处理中；针对线性调频连续波雷达中系统背景干扰和回波动态范围问题，创立了系统背景综合抑制技术和频域动态范围压缩技术，并将它应用于实孔线性调频连续波雷达系统中，显示出它们的有效性。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。